sklearn.linear_model.Ridge

class sklearn.linear_model.Ridge(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=0.001, solver='auto', random_state=None)[source]

Linear least squares with l2 regularization.

Minimizes the objective function:

||y - Xw||^2_2 + alpha * ||w||^2_2

This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Also known as Ridge Regression or Tikhonov regularization. This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape (n_samples, n_targets)).

Read more in the User Guide.

Parameters
alpha{float, ndarray of shape (n_targets,)}, default=1.0

Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to C^-1 in other linear models such as LogisticRegression or LinearSVC. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.

fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).

normalizebool, default=False

This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

max_iterint, default=None

Maximum number of iterations for conjugate gradient solver. For ‘sparse_cg’ and ‘lsqr’ solvers, the default value is determined by scipy.sparse.linalg. For ‘sag’ solver, the default value is 1000.

tolfloat, default=1e-3

Precision of the solution.

solver{‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’, ‘saga’}, default=’auto’

Solver to use in the computational routines:

  • ‘auto’ chooses the solver automatically based on the type of data.

  • ‘svd’ uses a Singular Value Decomposition of X to compute the Ridge coefficients. More stable for singular matrices than ‘cholesky’.

  • ‘cholesky’ uses the standard scipy.linalg.solve function to obtain a closed-form solution.

  • ‘sparse_cg’ uses the conjugate gradient solver as found in scipy.sparse.linalg.cg. As an iterative algorithm, this solver is more appropriate than ‘cholesky’ for large-scale data (possibility to set tol and max_iter).

  • ‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative procedure.

  • ‘sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses its improved, unbiased version named SAGA. Both methods also use an iterative procedure, and are often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

All last five solvers support both dense and sparse data. However, only ‘sparse_cg’ supports sparse input when fit_intercept is True.

New in version 0.17: Stochastic Average Gradient descent solver.

New in version 0.19: SAGA solver.

random_stateint, RandomState instance, default=None

The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when solver == ‘sag’.

New in version 0.17: random_state to support Stochastic Average Gradient.

Attributes
coef_ndarray of shape (n_features,) or (n_targets, n_features)

Weight vector(s).

intercept_float or ndarray of shape (n_targets,)

Independent term in decision function. Set to 0.0 if fit_intercept = False.

n_iter_None or ndarray of shape (n_targets,)

Actual number of iterations for each target. Available only for sag and lsqr solvers. Other solvers will return None.

New in version 0.17.

See also

RidgeClassifier

Ridge classifier

RidgeCV

Ridge regression with built-in cross validation

sklearn.kernel_ridge.KernelRidge

Kernel ridge regression combines ridge regression with the kernel trick

Examples

>>> from sklearn.linear_model import Ridge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> rng = np.random.RandomState(0)
>>> y = rng.randn(n_samples)
>>> X = rng.randn(n_samples, n_features)
>>> clf = Ridge(alpha=1.0)
>>> clf.fit(X, y)
Ridge()

Methods

fit(self, X, y[, sample_weight])

Fit Ridge regression model.

get_params(self[, deep])

Get parameters for this estimator.

predict(self, X)

Predict using the linear model.

score(self, X, y[, sample_weight])

Return the coefficient of determination R^2 of the prediction.

set_params(self, \*\*params)

Set the parameters of this estimator.
__init__(self, alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=0.001, solver='auto', random_state=None)[source]

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y, sample_weight=None)[source]

Fit Ridge regression model.

Parameters
X{ndarray, sparse matrix} of shape (n_samples, n_features)

Training data

yndarray of shape (n_samples,) or (n_samples, n_targets)

Target values

sample_weightfloat or ndarray of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight.

Returns
selfreturns an instance of self.
get_params(self, deep=True)[source]

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsmapping of string to any

Parameter names mapped to their values.

predict(self, X)[source]

Predict using the linear model.

Parameters
Xarray_like or sparse matrix, shape (n_samples, n_features)

Samples.

Returns
Carray, shape (n_samples,)

Returns predicted values.

score(self, X, y, sample_weight=None)[source]

Return the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the residual sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

Parameters
Xarray-like of shape (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns
scorefloat

R^2 of self.predict(X) wrt. y.

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters
**paramsdict

Estimator parameters.

Returns
selfobject

Estimator instance.